Microsoft Word - Article final.doc Adv Syst Sci Appl 2025; 2; 1-10 Published online at https://ijassa.ipu.ru. Computer Simulation of a Magnetic Separator for Iron Ore Dressing under Conditions of Uncontrolled Disturbances Nina Osipova* University of Science and Technology MISIS, Moscow, Russia Financial University under the Government of the Russian Federation, Moscow, Russia Abstract: The article presents a theoretical material about the principle of operation, design and advantages of the magnetic iron ore separator. A review of researches is given, where special attention is paid to the study of factors that affect the quality of concentrate and the loss of a valuable component in the tailings. The specification of the PDM-SC-120/300 magnetic separator is given. Regression models are obtained that reflect the relationship between the content of the class -0.074 mm and the solid phase flow rate in the separator feed with a high coefficient of determination. The statistical significance of this coefficient was verified using the Fisher criterion. A mathematical description of the object elements such as governing valve, motor, and magnetic separator is given. These models are simplified by dropping small time constants and linearization in the vicinity of nominal modes using Taylor series expansion. The main disturbances that cause the deviation of the dressing indicators from the optimal values are highlighted. A computer model of the magnetic separator was constructed using the Simulink Matlab application. The simulation results showed that with the specified control actions, an increase in the content of the class -0.074 mm in the feed to 94-95 % brings the mass fraction of iron in the concentrate to the acceptable limits but reduces the productivity of the separator. Keywords: magnetic separator, concentrate, tails, Matlab, MS Excel, regression model, Fisher criterion, correlation, coefficient of determination, Taylor series. 1. INTRODUCTION Over the past century, the constant growth of human needs for iron has led to the development and improvement of new technologies for ore dressing. The most widespread process is the magnetic separation. Its main purpose is to separate ore material particles into two phases: concentrate with a high iron content and tailings with a small fraction of the valuable component. By design the magnetic separator is made in the form of a drum that rotates at the given speed and a stationary magnetic system located in its inner part. Separation of the ore stream is based on the magnetic susceptibility of its constituent particles. If this parameter has a high value, then the particles stick to the drum and enter the concentrate compartment, and the rest, without attracting, are immediately washed off into the tailings compartment. The advantage of the magnetic dressing method is the ability to create a high force of attraction to the drum, which is hundreds of times higher than the particles weight, as well as safety during maintenance of the separator and harmlessness to the environment [5]. There are dry and wet magnetic dressing. In the first case, the ore is fed to the separator after preliminary crushing and screening. In the second case, after grinding in the mill and classification by size, the ore enters the magnetic separator in a mixture with a liquid (pulp). The above processes are multi-stage. * Corresponding author: nvo86@mail.ru 2 N. V. OSIPOVA Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) The iron ore raw material coming to the metallurgical plant in the form of agglomerate or pellets must be of the specified quality with permissible deviations from the norm established by technical conditions and regulations. Otherwise, you have to adjust the modes of melting units or spend more additional materials, which increases the cost of steel production. It is also necessary to ensure that iron losses in the tailings that do not exceed the permissible value. 2. REVIEW OF THE RESEARCH The main purpose of the research in the study of mineral processing is to identify the main factors that affect the iron content in the products of the magnetic separator, including controlling and disturbing influences. Control actions can be changed by a human operator or by an automatic system. Disturbing influences are random changes in the physical and mechanical properties of the ore or pulp. Several researches have been devoted to the study of the influence of controlling and disturbing influences on the magnetic separation process. In [1], multiple regression equations for a specific type of ore are obtained. One of them relates the iron content in the concentrate and the control variables: the filling level of the mill at the second stage of grinding, the density of the hydrocyclone discharge. Another is the association of loss of iron in the tails of the first stage of dressing and fill level of the mill, the water flow into the mill the first stage of grinding, drain density classifier. The coursebook [10] describes the principle of creating a regression model based on experimental planning, which can predict the mass fraction of iron in the concentrate for a predetermined step forward in time. This model is based on the calculated average iron content for a certain period, the deviation of the current value of the iron content from the average, and changes in the load on the ore section. The paper [4] presents a regression model, in which the dependent variable is the iron mass fraction in the enrichment products, and the factors are the load on the industrial product of dry magnetic separation, water flow into the classifying apparatus and magnetic separators at the 1st, 2nd, 4th stages of dressing. The disadvantage of these methods is a large delay between obtaining of input and output variables, which makes it difficult to quickly update the coefficients of the regression model and calculate the control variables. The above papers do not specify what specific disturbances can cause deviations of the dressing indicators from the set ones. In [6], static characteristics of magnetic separators are given, reflecting the dependence of the iron content in the concentrate and its losses in the tailings on the drum rotation speed and pulp density, which can be controlled by supplying additional water to the separator bath. However, the graphs do not indicate the numerical values on the axes and the equations that they were based on. It is only known that in a wide range of parameters, the dependencies are nonlinear, close to the second-order polynomial. Therefore, it is necessary to solve the following problems: to select the control and disturbing effects that affect the content of the useful component in the concentrate and in the tailings, so that there is no lag between the input and output of the object; to develop a computer model of the magnetic separator, which allows to study its operation of the separator under nominal control effects under conditions of uncontrolled disturbances. 3. OBJECT OF RESEARCH The object of research is the drum semi-countercurrent magnetic separator PDM-SC-120/300, which is used in many iron ore mining and processing plants to separate particles of less than 1 mm in size at the final stages of dressing. It’s required for simulation specification is given in Table 3.1 [2]. COMPUTER SIMULATION OF A MAGNETIC SEPARATOR FOR IRON ORE ENRICHMENT 3 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) Table 3.1. Specification of the PDM-SC-120/300 magnetic separator Feed option Drum rotation speed, min-1 Permissible productivity for solid phase, tons/h Content in the feed separator, % Class -0.074 mm Solid phase of the pulp 1 60-70 30 140-180 2 20 80-120 3 75-85 30 100-140 4 20 70-100 5 94-96 30 60-80 6 20 40-60 As you can see from the table, there are six separator feed options. In this case, the disturbing effects are the content in the feed of the class -0.074 mm and the of solid phase flow rate (productivity) at two limit values of the solid phase content in the pulp. Before finding the degree of influence of factors on the dressing indicators, it is necessary to check their correlation. For this purpose, MS Excel generated samples of random variables with a normal distribution law that characterize the content of the class -0.074 mm and the corresponding solid phase flow rate for two values of the solid phase content in the separator feed (Table 3.2). Table 3.2. Characteristics of random values of disturbances for simulation in MS Excel Solid phase content in pulp, % Mathematical expectation Maximum deviation (3σ) Standard deviation (σ) Performance, tons/h The content of the class -0.074 mm, % Performance, tons/h The content of the class -0.074 mm, % Performance, tons/h The content of the class -0.074 mm, % 20 100 65 20 5 20/3 5/3 30 160 20 85 80 15 15/3 30 120 20 20/3 20 50 95 10 1 10/3 1/3 30 70 For each of the above six options, the sample consists of 10 values, i.e. 30 positions for the solid phase content in the feed, equal to 20 % and 30 %. The diagram with the trend line based on the linear dependence is presented and the coefficient of determination is calculated (Fig. 3.1). Fig. 3.1. Correlation diagram of solid phase flow rate and -0.074 mm class content in the separator feed The high determination coefficients R1 2 = 0,9134 и R2 2 = 0,9767 indicate a strong dependence of the solid phase flow rate on the content of the class -0.074 mm in the 4 N. V. OSIPOVA Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) separator feed. Let’s evaluate the statistical significance of the coefficients using the Fischer criterion. In the first case, we find the observed F-value for two dependencies: 2 1 1 2 1 2 2 2 2 2 0.9134 28 38.55, 1 1 0.9134 1 0.9767 28 1173.72, 1 1 0.9767 1 R f F R m R f F R m           (3.1) where n = 30 is the number of experimental points; m = 1 is the number of factors; f = n-m-1 is the number of degrees of freedom; α = 0.05 is the level of significance. It turns out that the found value is greater than the critical value indicated in the table Fcr = 4.2 (F1 > 4.2; F2 > 4.2), which confirms the statistical significance of R2 with a probability P =1 - α = 0.95. Therefore, if there is a correlation in the mathematical model, it is sufficient to use just one of the disturbances: the solid flow rate or the content of the class -0.074 mm in the feed of the separator. 4. COMPUTER MODEL OF A MAGNETIC SEPARATOR 4.1 Nonlinear Dynamic Model of a Magnetic Separator As control variables, we will use the water flow rate into the separator bath and the rotation speed of its drum. This choice is justified by the absence of a lag between these impacts and the output indicators, as well as the fact that there is no need to change the separator design. The model block diagram is shown in Figure 4.1. When controlling the degree of the valve opening and the motor shaft rotation speed by setting different values εs and ωs, the water flow rate into the bath Wb and the rotation speed of the drum ω, respectively, are regulated. It causes a change in the content of magnetite iron in the concentrate β and tailings ν monitored by analyzers. The parameter ξ is a disturbance that characterizes the instability of the physical and mechanical properties of the pulp, which also causes fluctuations in the dressing indicators β and ν. Fig. 4.1. Block diagram of the magnetic separator model Let’s look at the individual components of the model in detail. The model of the governing valve is described by the following differential equation: v v v s ( ) ( ) , d t T t dt      (4.1) COMPUTER SIMULATION OF A MAGNETIC SEPARATOR FOR IRON ORE ENRICHMENT 5 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) εs is the set value for the degree of opening of the valve, %; εv is the current value of the valve opening degree, %; Tv is the time constant of the controlled valve, sec. For the most valves, Tv is approximately 0.3 seс [7]. The water flow rate in the separator bath is related to the value εv and the ratio [9]: b v( ) 11 ( ).W t t  (4.2) The model of an asynchronous drive motor has a very complex mathematical description in the form of a system of nonlinear equations. However, in the case of operation in a small neighborhood of the point that corresponds to the rated mode, it is allowed to consider a linearized system equivalent to the DC motor model: m m m s ( ) ( ) , d t T t dt    (4.3) ωs is the set value of the motor drive shaft rotation speed, min-1; ωm is the current value of the motor drive shaft rotation speed, min-1; Tm is the time constant of the drive motor, s. The model of the gearbox is determined based on the ratio of the nominal rotation speed of the separator drum ωs.nom = 19 min–1 and the motor ωm.nom = 1000 min –1: s.nom m.nom ω 19 0.02. ω 1000g k    (4.4) The rotation speed of the separator drum ωg using a reducer is equal to: mgω ( ) 0.0 .2ω ( )t t (4.5) According to the simulation of asynchronous motors the value of Tm can be assumed to be equal to 0.03 seс [9]. The models must have "dead zones" Δv and Δm for the valve and drive, respectively. This means that if the input signal is |εv|≤ Δv or |ωg|≤ Δm, then the output signal is ε = 0, ω = 0, otherwise ε = εv - Δv or ω = ωg – Δm. Let’s take Δv = 3 %, Δm = 0,1 %. The dynamics of the content of magnetite iron in the concentrate and tailings is governed by the following system of differential equations: β β β β β ν ν ξ ξ v v ν β 1 1 1 β ,ω ( ) (ξ) ( ) ( , ν 1 1 1 ν ,ω ξ), d f W f dt T T T d f W f dt T T T      (4.6) where W = Wl + Wb is the sum of the liquid phase consumption in the pulp and the water consumption in the separator bath, fβ(W, ω) и fν(W, ω) describe the relationship of the dressing indices β, ν and the control variables W, ω and the control variables W, ω in steady state when βd dt = 0 и ν d dt = 0: 2 2 β 2 2 ν , ω – 0.0000042 0.0082 – 0.023ω 1.21ω 46.5, , ω – 0.0000025 0.0087 0.035ω – 1.3ω 10.2, ( ) ( ) f W W W f W W W         (4.7) where Tβ, Tv are the time constants of magnetic separator (sec), Tβ = 1…10 sec, Tv = 1...10 seс [7]; fβξ(ξ), fνξ(ξ) are the functions on uncontrolled disturbances ξ. To simplify the simulation, we put Tβ = Tv = 1 sec. The system (4.7) is obtained in [9] based on the reference data of the average concentration of iron ore mining and processing plants, provided that fβξ(ξ) = const, fνξ(ξ) = const. The units of measurement for W and ω are m3/h and min-1 respectively. 6 N. V. OSIPOVA Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) 4.2 Linearization of the Magnetic Separator Model For the convenience of research, simulation and automation of the magnetic separator, we linearize equations (4.6). The most of automatic systems are designed and configured under the assumption that the object under control is linear. Using the rule for calculating the function increment Δy = y'Δx, we perform the system linearization by expanding the Taylor series of equations (4.6) in the vicinity of the nominal modes (Wnom, ωnom) with respect to Δβ and Δν with the rejection of nonlinear terms. Given that Tβ = Tv = 1 seс and that fβ(W, ω), fν(W, ω) are found by equation (4.7), we obtain: nom nom nom nom nom nom nom nom β β – 2 0.0000042 0.0082 – 2 0.023ω ω 1.21 ω= = β – 0.0000084 0.0082 – 0.046ω ω 1.21 ω, ν ν – 2 0.0000025 0.0087 2 0.035ω ω-1.3 ω ν – 0.000005 0.0087 0.07ω ω – W W W W W W W W W W W W                                        1.3 ω. (4.8) For simulation, we assume that the required content of magnetite iron in the concentrate βs = 63.8 %, which is the average for many iron ore mining and processing plants [2]. Substituting ωnom = 19 min-1 in the first equation in (4.7) for fβ(Wnom, ωnom) = βs, we get Wnom = 400 m3/h. Then the loss of magnetite iron in the tailings at Wnom, ωnom is fν(Wnom, ωnom) = νs = 1.22 %. Assuming the time constants of the valve and motor are negligible in compare with the time constants of the magnetic separator, the water flow rate into the separator bath is associated with a given degree of opening of the valve as W = 11εs, and the rotation speed of the drum is determined by the equality ω = ωs. We introduce new notation for the variables Δβ = x1, Δν = x2, ΔW = u1, Δω = u2. We assume that the change ΔW is due to the control of the valve. Is due to the control of the valve. Taking into account the above, substituting Wnom, ωnom in equation (4.8), we get: 1 1 1 2 2 2 1 2 0.00484 0.336 , 0.0067 0.03 x u u x u x x u          (4.9) or in matrix form: ( ) ,( ) ( )t x tx tA Bu  (4.10) where: 1 0 0.0048 0.336 , . 0 1 0.0067 0.03 A B             (4.11) The linear representation of the system (4.7) in the interval (Wnom, ωnom) has the form:         β nom nom βlin β nom nom nom β nom nom nom ν nom nom νlin ν nom nom nom ν nom nom nom , ω ) , ω , ω ) , ω ) ω ω 55.48 0.00484 0.336ω, ω , ω ) , ω , ω ) , ω ) ω ω 2.035 0.0067 0. ( ( ) ( ( ( ( ) ( 03ω. ( ω f W f W f W W W W f W W f W f W f W W W W f W W                            (4.12) As a disturbance, we will consider the change in the percentage q of solid and the solid phase flow rate in the feed q. As can be seen from Table 4.1, the separator maximum performance is Q = 180 tons/h with a percentage of solid q = 30 %, and the minimum - Q = 40 tons/h with a solid q = 20 %. Let’s calculate the minimum and maximum values of the liquid phase flow rate in the pulp, taking into account that the water density ρw = 1 ton/m3: COMPUTER SIMULATION OF A MAGNETIC SEPARATOR FOR IRON ORE ENRICHMENT 7 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025)       l w 3 l.min 3 3 l.max 3 100 % , 100 % 30 % 40 tons/h 93.3 m /h, 1 ton/m 30 % 100 % 20 % 180 tons/h 720 m /h. 1 ton/m 20 % q W Q q W W                (4.13) Substituting W = Wb + Wl in (4.12) and replacing the liquid phase flow rate of the with the expression from equation (4.13), we get:     ξ ξ βlin b β νlin b ν β l ν ξ w ξ w l ( ) ( , ) ( ) ( , ω 55.48 0.00484 0.336ω+ , , ω 2.035 0.0067 0.03ω+ 0.00484 , ), 100 ( , ) , 100 ( , ) 0.00484 0.0067 0.0067 . f W W f f W W f f q Q q Q q q Q Q q q q Q Q q W f W                    (4.14) According to the specifications, the permissible deviation for the content of magnetite in the concentrate x1,2max ≤ 1 %. Then βmin = 63.8 % - 1 % = 62.8 %, βmax = 63.8 % + 1 % = 64.8 %. Obviously, the minimum losses in the tailings are 0. Their limit is νlim = 1.22 % + 1 % = 2.22 %. Then the deviation x2max = 1 %. Consider the procedure for determining the upper limits on control actions. The main requirement for the linear representation of the model (4.7) is that at the boundary values of ±u1,2max, the absolute value of the difference in the dressing indicators calculated from the nonlinear and linearized models should be equal to the error of their measurement. According to Russian Standard, it is 0.9 % for magnetite iron in concentrate and 0.3 % for losses in tailings during laboratory research by chemical analysis [3]. Let the error of the analyzers also be equal to these values, then restrictions can be found from the solution of the system: β nom 1max nom 2max βlin nom 1max nom 2max ν nom 1max nom 2max νlin nom 1max nom 2max ( ) ( ) ( , ω + - , ω + 0.9, , ω + - , ω + 0) ) 3.( . f W u u f W u u f W u u f W u u          (4.15) The expressions fβlin(Wnom + u1max, ωnom + u2max), fνlin (Wnom + u1max, ωnom + u2max) are found by substitution in (4.12) Wnom + u1max, ωnom + u2max instead of W, ω: β nom nom β nom nom βlin nom 1max nom 2max β nom nom 1max 2max ν nom nom ν nom nom νlin nom 1max nom 2max nom nom 1max 2max , ω ) , ω ) , ω + , ω ) , ω , ω ) , ω ) , ω + ( ( ( ) ( ( ( , ω ) . ω ( ) ( f W f W f W u u f W u u W f W f W f W u u f W u u W                 (4.16) The system (4.16) is easily solved using the Matlab computing package of the Optimization toolbox application. In this case, among the real roots, u1max = ± 346.83 m3/h, u2max = ± 4.14 min-1. So Wnmin = 400 m3/h -346.83 m3/h = 53.2 m3/h, Wnmax = 400 m3/h + 346.83 m3/h = 746.8 m3/h, ωnmin = 19 min-1 - 4.14 min-1 = 14.86 min-1, ωnmax = 19 min-1 + 4.14 min-1 = 23.14 min-1, the following restrictions must be met: Wnmin ≤ W ≤ Wnmax and ωnmin ≤ ω ≤ ωnmax. The nominal value of degree of opening of the valve εnom = 36.36 %, which corresponds to W = 400 m3/h. We will assume that the data from the analyzers is transmitted with a very small delay, the voltage at the output of their microchip is related to the physical value through a coefficient equal to one. Therefore, we will not take them into account in the model. 8 N. V. OSIPOVA Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) The diagram of the computer model of the magnetic separator is shown in Fig. 4.2. It was also built using the Matlab environment of the Simulink application based on the block diagram from Fig. 4.1. Fig. 4.2. Diagram of a computer model of a magnetic separator in Matlab Simulink 4.3 Simulation Result The simulation was performed as follows. Disturbances were periodically fed to the input of the object at an interval equal to the end time of transients of the magnetic separator tend = 5 seс [8]: the change in the percentage of solid in the feed and the solid phase flow rate, which was set using a random number generator in the range according to Table 4.1, i.e., six variants of pulp properties were modeled. Let’s take the first option as an example. When the solid content in the feed is 30 %, the solid phase flow rate increases to 120 tons/h. The model calculates the water consumption in the pulp using the equation (4.13), which becomes equal to Wl = 280 m3/h, which is within the range of Wlmin ≤ Wl ≤ Wlmin. The change in this signal is fed to the magnetic separator model (4.14) and used in the functions fβξ(q, Q), fνξ(q, Q) (Fig. 4.3). Fig. 4.3. Changing the liquid and solid phases flow rate in the pulp COMPUTER SIMULATION OF A MAGNETIC SEPARATOR FOR IRON ORE ENRICHMENT 9 Copyright ©2025 ASSA. Adv. in Systems Science and Appl. (2025) Fig. 4.4. The content of magnetite iron in the concentrate and tailings when the properties of the pulp are unstable In the absence of automatic control of the separator, constant nominal values of water flow rate Wb = 400 m3/h and rotation speed ω =19 min-1. The following conditions are met: Wnmin ≤ W ≤ Wnmax. The content of magnetite iron in the concentrate in the time interval of 5- 20 seс is greater than the value of βmax. The same can be said for tailings that are superior to the νlim. The largest of the bursts is β = 65.34 % и ν = 3.35 % (Fig. 4.4). This corresponds to the content of the class -0.074 mm in the feed of 60-70 %. Only after t = 20 sec, the iron content falls below βmax, when the pulp is 94-95 % of the class -0.074 mm, but there is a sharp decrease in the productivity of the separator, which becomes below 80 tons/h. 5. CONCLUSION As control actions were selected the rotation speed of the magnetic separator drum and the water flow rate into its bath. The nominal operating modes corresponding to the specified dressing parameters in the absence of disturbances are determined by the content and the solid phase flow rate in the feed, which correlates with the content of the class -0.074 mm in the feed, are taken as the parameters. A computer linear dynamic model of the separator in the Matlab Simulink package is constructed. Based on the results of the simulation, the following conclusions can be drawn. Setting control actions with constant nominal values is not enough to stabilize the quality of iron ore concentrate. When changing the content of the class -0.074 mm in the feed in the range from 60 % to 85 %, the separator operates with a sufficiently high performance, but the iron content in the concentrate is higher than normal. The same can be said about tailings. Increasing the content of the class -0.074 mm in the feed to 94-95 % brings the mass fraction of iron in the concentrate to the acceptable limits but reduces the productivity of the separator. Therefore, controlling the grinding and classification processes before magnetic separation in order to stabilize the granulometric composition is not promising. 10 N. V. OSIPOVA Copyright ©2025 ASSA Adv. in Systems Science and Appl. (2025) A more rational approach is to create an optimal control system. It should be based on the formulated criterion for minimizing deviations of the iron content in the concentrate and tailings relative to the set values with restrictions on the control variables selected based on the permissible linearization error at the boundaries of their change intervals. In the future, the model of optimal control of the magnetic separator will allow evaluating and predicting the possibility of maintaining the quality of iron ore concentrate with acceptable deviations. This will reduce the number of experiments in laboratory and industrial installations and thus increase their service life and reduce the number of consumables. REFERENCES 1. Anikin, A. I. (1984). Research and development of an optimal control system for a section of a self-grinding magneto-concentrating plant as a subsystem of the automated control system of the Lebedinsky MPP KMA. Ph.D. Thesis, Leningrad Order of Lenin, order of the October Revolution and Order of the red banner of labor Plekhanov mining Institute 2. Bogdanov, O. S. (1984) Spravochnik po obogashcheniyu rud. Obogatitel'nye fabriki (Tom 4) [Handbook of ore dressing. Processing plants (Volume 4)]. Moscow, USSR: Nedra, [in Russian]. 3. GOST 16589-86 (1987) Rudy zheleznye tipa zhelezistyh kvarcitov. Metod opredeleniya zheleza magnetita [Iron ores of the ferruginous quartzite type. Method for determining iron magnetite]. Moscow, USSR [in Russian]. 4. Kazakov Y. M. (1994) Control of the wet magnetic dressing process line. Ph.D. Thesis, Ural state mining and geological Academy 5. Karmazin, V. V., (2013). Problemy i perspektivy magnitnogo obogashcheniya [Problems and prospects of magnetic dressing]. Gornyj informacionno-analiticheskij byulleten', S1, 560–575, [in Russian] 6. Maryuta A. N., Kachan YU. G., Bun'ko V. A. (1983) Avtomaticheskoe upravlenie tekhnologicheskimi processami obogatitel'nyh fabrik [Automatic management of technological processes in concentrating plants] Moscow, USSR: Nedra, [in Russian]. 7. Osipova N. V. (2018). Ispol'zovanie fil'tra Kalmana pri avtomaticheskom kontrole pokazatelej magnitnogo obogashcheniya zheleznyh rud [The use of Kalman filter in automatic control of indicators of iron ores magnetic concentration], Izvestiya Visshikh Uchebnykh Zavedenii. Chernaya Metallurgiya = Izvestiya. Ferrous Metallurgy, vol. 61, iss. 5, 372-377. DOI: https://doi.org/10.17073/0368-0797-2018-5-372-377 8. Osipova N. V. (2018). Sintez asimptoticheskogo nablyudatelya dlya sistemy upravleniya magnitnym separatorom pri obogashchenii zheleznoj rudy [Synthesis of asymptotic observer for magnetic separator control in iron ore processing] Gornyj informacionno- analiticheskij byulleten', no 6, 153-160, [in Russian] DOI: 10.25018/0236-1493-2018-6- 0-153-160 9. Osipova N. V. (2018). Model of stabilization of the quality of iron-ore concentrate in the process of magnetic separation with the use of extreme regulation, Metallurgist, vol. 62, nos. 3-4, 303-309. DOI 10.1007/s11015-018-0660-8 10. Vinogradov, S. V. (1984) Avtomatizaciya tekhnologicheskih processov gornogo proizvodstva [Automation of technological processes of mining production]. Moscow, USSR: Nedra, [in Russian].